My condolences on your husband's passing.
Assuming these bills are yours, and not your husband's (if they are his, his estate is liable for them, not you), there are a number of things a creditor can do, but not until they sue you and get a judgment. A good description of the process may be found on the Court's website at http://www.the3rdjudicialdistrict.com/Small_Claim_Pl_Collect.htm.
They cannot garnish your social security.
You may want to speak with a local bankruptcy attorney. You might want to contact Seth Plats, a member of the National Association of Consumer Bankruptcy Attorneys (NACBA), at http://www.twinfallsattorneys.com/.
The best of luck to you.
If you do not pay your bills, they could sue you. They could even get a judgment against you. If you have assets that aren't protected by statute, they could attach liens to those assets.
I strongly encourage you to gather your bills and go sit down with a consumer bankruptcy attorney. I know someone in Idaho who practices in that area of the law and she may be able to assist you.
Most states exempt certain assets from collection,so your house and your car are likely partially or fully protected. However, usually money in bank accounts is not fully protected. Talk to a bankruptcy lawyer in your state about what is exempt from collection and then you can determine whether bankruptcy is your best option.
My condolences on your loss, and also for being forced to navigate knotty financial issues at this difficult time.
Your first three answers were from attorneys who do not practice in Idaho, so the value of those answers must be discounted heavily. (One of them gave you a link to a website for a court 150 miles away!) The only useful things said so far are: your liability may be limited, and you need the precise advice of local consumer-rights counsel. You will want to find a Twin Falls attorney particularly experienced in probate, community property, and creditors rights/bankruptcy law. That attorney will need to be adept at proving separate debt. the cost of the consultation you need should be modest.
Best wishes for a favorable outcome, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.